The Center for American Progress, a liberal think tank closely aligned with the White House, is embroiled in a dispute with several Jewish organizations over charges that some center staffers have publicly used language that could be construed as anti-Israel or even anti-Semitic.

The controversy could add to divisions over Middle East policy among groups that are key political allies of President Obama, potentially complicating the president’s reelection outreach to some Jewish voters, just as he seeks to assure them of his commitment to Israel’s security amid fears of an Iran nuclear threat.

Officials at CAP, which publishes research and writing on many subjects, said the “inappropriate” language came only in personal tweets — not on CAP’s Web site or its ThinkProgress blog. The tweets were deleted, and the authors apologized.

Among the points of contention are Twitter posts by one CAP writer on his personal account referring to “Israel-firsters.” Some experts say the phrase has roots in the anti-Semitic charge that American Jews are more loyal to a foreign country, Israel, than to the United States. In another case, a staffer described a U.S. senator as showing more fealty to the prime U.S. pro-Israel lobby, the American Israel Public Affairs Committee, than to his own constituents. The first writer has since left the staff.

But the critics also point to writings on the CAP Web site, where staffers have suggested that AIPAC was pushing the United States toward war with Iran and likened Israel’s treatment of Palestinians in the Gaza Strip to the policies of the segregated American South.

One reason the comments are drawing special scrutiny is because CAP is an idea generator for Obama’s Washington. CAP’s chairman and former president, John Podesta, is a part-time adviser to the State Department and a onetime chief of staff in the Clinton White House. There is no indication that he was involved with the controversial material.

Some major Jewish groups have demanded corrective action by the think tank and asked for answers from friends in the White House.

“The language is corrosive and unacceptable,” said Rabbi Abraham Cooper, associate director of the Simon Wiesenthal Center. He added that the blog posts and tweets from CAP staffers “are the responsibility of the adults who run the place, not only the kids who play.”

Cooper conveyed his concerns about CAP during a White House meeting last week with Obama’s newly appointed Jewish community liaison, Jarrod Bernstein, who told Cooper that the situation at CAP was “troubling” and not reflective of “this administration.”

CAP officials say the incidents in question were an anomaly.

“The clear and overwhelming record of the literally hundreds of articles and policy papers from the Center for American Progress and ThinkProgress demonstrates our longstanding support both for Israel and the two-state solution to the Middle East peace process as being in the moral and national security interests of the United States,” Ken Gude, chief of staff for CAP, wrote in an e-mail response to questions from The Post.

“We have a zero-tolerance policy for racism, sexism, anti-Semitism or any form of discrimination,” Gude wrote.

Zaid Jilani, the author of the “Israel-firster” tweets, apologized and left CAP’s staff in recent days to take another job. Jilani could not be reached for comment.

Center officials tried to address concerns over an August ThinkProgress post titled “AIPAC’s Iran Strategy On Sanctions Mirrors Run-Up To Iraq War Tactics.” An update asserted that “we are not reporting on whether AIPAC lobbied for the Iraq war” and that the center is “very concerned about Iran’s nuclear program.”

Gude, in an e-mail, added that CAP does not believe AIPAC is pushing for war with Iran. “Iran’s policy choices are driving this situation, not anyone or any group in the United States,” he wrote.

Some progressive advocates who work closely with CAP dismiss the charges. “We are baffled and appalled by the charges of anti-Semitism that some have leveled at CAP,” wrote Matt Bennett, a spokesman for Third Way, an advocacy organization devoted to promoting centrist ideas.

David Harris, president of the National Jewish Democratic Council, described CAP’s views on Israel and Iran as reflecting “mainstream positions and concerns of the American Jewish community — and indeed of most Americans.”

A White House spokesman, Matt Lehrich, declined to comment on CAP. “Anyone who wants to know where the president stands need look no further than his own words and actions,” Lehrich said, adding that Obama “has repeatedly reiterated America’s unshakable commitment to Israel’s security and stood up against attempts to single out Israel in international forums.” He said that the administration has “ratcheted up unprecedented pressure on Iran.”

The critics are not mollified.

Abraham Foxman, national director of the Anti-Defamation League, said some of the statements from CAP staffers “are anti-Semitic and borderline anti-Semitic.”

“We’re concerned about it because this is a serious think tank, and it does influence the administration,” Foxman added.

Jason Isaacson, of the American Jewish Committee, said he was concerned by “very troubling things that have been written on a pretty regular basis by certain people associated with the organization.”

“For any serious policy center there are certain lines of fairness and objectivity and good sense that should not be crossed, and yet, disturbingly, those lines have regularly been crossed,” he added.

The controversy could add friction to the already tense relationship between Obama and many pro-Israel Jews, a constituency the president has courted for donations and political support.

Significant Jewish population centers are targets for Obama’s campaign in the battleground states of Florida, Ohio, and Pennsylvania, and one of the campaign’s earliest hires was a Jewish outreach coordinator. Obama won nearly eight in 10 Jewish votes in 2008. Gallup polling shows his approval rating among Jews as of last month standing at 57 percent, 14 points higher than his overall approval rating.

Complicating the calculation is that many liberals have grown more critical of Israel’s policies as the government there has turned more to the right. Some young liberal Jews are expressing disaffection with a country their parents had taught them to revere.

At the same time, Israel’s supporters worry that greater instability in the Middle East and Iran’s quest for nuclear technology pose threats to Israel.

Those differences have grown more evident since the CAP controversy began in early 2011, when Jewish groups started quietly bringing complaints to center officials.

Last month, Josh Block, a former AIPAC spokesman and Clinton administration official, distributed a compilation of CAP staffers’ writings and other public statements that he said amounted to an “outrageous vilification of pro-Israel Americans.”

Some on the left argue that charges of anti-Semitism such as those being leveled at CAP shut down needed policy debates.

Jeremy Ben-Ami, president ofJ Street, a left-leaning voice on Israel issues, said he had no problem with “Israel-firster.”

“If the charge is that you’re putting the interests of another country before the interests of the United States in the way you would advocate that, it’s a legitimate question,” Ben-Ami said.

Ben-Ami added that Jewish groups “should tread lightly” when they make accusations of anti-Semitism. “Because when they do need to use that word, people won’t take you seriously,” he said.

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